Question

A $2kg$ block slides on a horizontal floor with a speed of $4m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction is $15N$ and spring constant is $10,000N/m$. The spring compresses by (in cm)

• A. $8.5$
  
• B. $5.5$
  
• C. $2.5$
  
• D. $11.5$
  

Answer 1

The correct option is B $5.5$

By conservation of energy

$\Rightarrow 0.5\times m{v}^2=0.5\times k{x}^2+F_{friction}x$

$\Rightarrow 0.5\times 2\times 4^2=0.5\times 10000\times x^2+15x$

$\Rightarrow 16=5000x^2+15x$

$\Rightarrow x=0.055m$

$\Rightarrow x=5.5m$

Hence correct answer is option $B$